Here's how an undercarriage is designed: there is a plane mass and descent speed, which gives a certain kinetic energy which must be absorbed by deformations ( tyres and u/c bits)...
!/2MVsquared = av.force times deformation.
That is, energy of landing /amount of deformation built in = forces in u/c.
There is ( was ) no requirement for damping in JAR22 or whatever it is called these days, but Nev is correct to say that damping makes an easier plane to land. Shock absorbers do the damping in a road car. The Jabiru, for one, has no real built-in damping. The flexing of the legs and the squashing of the tyres provide the deformation needed.
Jabirus were tested by loading them up to max weight with bags of stuff and then dropping them a metre onto a greased floor.Then the height of the plane was re-measured to see if there was any change. If the plane had failed this test, Rod Stiff would have lost his house.